Local Buckling of a Circular Interface Delamination Between a Layer and a Substrate With Finite Thickness

1999 ◽  
Vol 67 (3) ◽  
pp. 590-596 ◽  
Author(s):  
R. Sburlati ◽  
E. Madenci ◽  
I. Guven
Keyword(s):  
Integral Equations ◽  
Mixed Boundary ◽  
Finite Thickness ◽  
Local Buckling ◽  
Singular Integral Equations ◽  
Mixed Boundary Conditions ◽  
Homogeneous System ◽  
Theory Of Elasticity ◽  
Cauchy Type ◽  
The Stability

An analytical study investigating the local buckling response of a circular delamination along the interface of an elastic layer and a dissimilar substrate with finite thickness is presented. The solution method utilizes the stability equations of linear theory of elasticity under axisymmetry conditions. In-plane loading and the presence of mixed boundary conditions on the bond-plane result in a homogeneous system of coupled singular integral equations of the second kind with Cauchy-type kernels. Numerical solution of these integral equations leads to the determination of local buckling stress and its sensitivity to geometric parameters and material properties. [S0021-8936(00)01503-8]

Plane Analysis of Finite Multilayered Media With Multiple Aligned Cracks—Part I: Theory

2006 ◽  
Vol 74 (1) ◽  
pp. 128-143 ◽  
Author(s):  
Linfeng Chen ◽  
Marek-Jerzy Pindera
Keyword(s):  
Integral Equations ◽  
Singular Integral ◽  
Mixed Boundary ◽  
Plane Deformation ◽  
Singular Integral Equations ◽  
Cauchy Type ◽  
Algebraic Equations ◽  
Energy Release Rates ◽  
Global Stiffness Matrix ◽  
Bounding Surfaces

Elasticity solutions are developed for finite multilayered domains weakened by aligned cracks that are in a state of generalized plane deformation under two types of end constraints. Multilayered domains consist of an arbitrary number of finite-length and finite-height isotropic, orthotropic or monoclinic layers typical of differently oriented, unidirectionally reinforced laminas arranged in any sequence in the plane in which the analysis is conducted. The solution methodology admits any number of arbitrarily distributed interacting or noninteracting cracks parallel to the horizontal bounding surfaces at specified elevations or interfaces. Based on half-range Fourier series and the local/global stiffness matrix approach, the mixed boundary-value problem is reduced to a system of coupled singular integral equations of the Cauchy type with kernels formulated in terms of the unknown displacement discontinuities. Solutions to these integral equations are obtained by representing the unknown interfacial displacement discontinuities in terms of Jacobi or Chebyshev polynomials with unknown coefficients. The application of orthogonality properties of these polynomials produces a system of algebraic equations that determines the unknown coefficients. Stress intensity factors and energy release rates are derived from dominant parts of the singular integral equations. In Part I of this paper we outline the analytical development of this technique. In Part II we verify this solution and present new fundamental results relevant to the existing and emerging technologies.

Load Buckling of a Layer Bonded to a Half-Space With an Interface Crack

1995 ◽  
Vol 62 (1) ◽  
pp. 64-70 ◽  
Author(s):  
Wen-Xue Wang ◽  
Yoshihiro Takao
Keyword(s):  
Half Space ◽  
Interface Crack ◽  
Integral Transform ◽  
Local Buckling ◽  
Compressive Load ◽  
Singular Integral Equations ◽  
Fourier Integral ◽  
Theory Of Elasticity ◽  
Layered System ◽  
Cauchy Type

An analytical solution is presented for local buckling of a model of delaminated composites, that is, a layer bonded to a half-space with an interface crack. The layered system is subjected to compressive load parallel to the free surface. Basic stability equations derived from the mathematical theory of elasticity are employed to study this local buckling behavior. They are different from the conventional buckling equations used in most previous studies and based on the classical structural mechanics of beams and plates. A system of homogeneous Cauchy-type singular integral equations of the second kind is formulated by means of the Fourier integral transform and is solved numerically by utilizing Gauss-Chebyshev integral formulae. Numerical results for the buckling load and shape are presented for various delamination geometries and material properties of both the layer and half-space.

On the receding contact between a graded and a homogeneous layer due to a flat-ended indenter

2021 ◽  
pp. 108128652110431
Author(s):  
Rui Cao ◽  
Changwen Mi
Keyword(s):  
Finite Element ◽  
Contact Problem ◽  
Integral Equations ◽  
Singular Integral ◽  
Functional Dependence ◽  
Singular Integral Equations ◽  
Homogeneous Layer ◽  
Cauchy Type ◽  
Receding Contact ◽  
Contact Pressures

This paper solves the frictionless receding contact problem between a graded and a homogeneous elastic layer due to a flat-ended rigid indenter. Although its Poisson’s ratio is kept as a constant, the shear modulus in the graded layer is assumed to exponentially vary along the thickness direction. The primary goal of this study is to investigate the functional dependence of both contact pressures and the extent of receding contact on the mechanical and geometric properties. For verification and validation purposes, both theoretical analysis and finite element modelings are conducted. In the analytical formulation, governing equations and boundary conditions of the double contact problem are converted into dual singular integral equations of Cauchy type with the help of Fourier integral transforms. In view of the drastically different singularity behavior of the stationary and receding contact pressures, Gauss–Chebyshev quadratures and collocations of both the first and the second kinds have to be jointly used to transform the dual singular integral equations into an algebraic system. As the resultant algebraic equations are nonlinear with respect to the extent of receding contact, an iterative algorithm based on the method of steepest descent is further developed. The semianalytical results are extensively verified and validated with those obtained from the graded finite element method, whose implementation details are also given for easy reference. Results from both approaches reveal that the property gradation, indenter width, and thickness ratio all play significant roles in the determination of both contact pressures and the receding contact extent. An appropriate combination of these parameters is able to tailor the double contact properties as desired.

Partial slip contact analysis for a monoclinic half plane

2020 ◽  
pp. 108128652096283
Author(s):  
İ Çömez ◽  
Y Alinia ◽  
MA Güler ◽  
S El-Borgi
Keyword(s):  
Integral Equations ◽  
Half Plane ◽  
Singular Integral ◽  
Integral Transform ◽  
Mixed Boundary ◽  
Normal Load ◽  
Fibrous Composite ◽  
Singular Integral Equations ◽  
Contact Stresses ◽  
Partial Slip

In this paper, the nonlinear partial slip contact problem between a monoclinic half plane and a rigid punch of an arbitrary profile subjected to a normal load is considered. Applying Fourier integral transform and the appropriate boundary conditions, the mixed-boundary value problem is reduced to a set of two coupled singular integral equations, with the unknowns being the contact stresses under the punch in addition to the stick zone size. The Gauss–Chebyshev discretization method is used to convert the singular integral equations into a set of nonlinear algebraic equations, which are solved with a suitable iterative algorithm to yield the lengths of the stick zone in addition to the contact pressures. Following a validation section, an extensive parametric study is performed to illustrate the effects of material anisotropy on the contact stresses and length of the stick zone for typical monoclinic fibrous composite materials.

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